Final answer:
The work output per cycle of the Carnot engine operating between reservoirs at 704 K and 300 K, with an absorption of 100 J from the hot reservoir, is 57.39 J.
Step-by-step explanation:
The question involves a Carnot engine operating between two reservoirs at different temperatures and determining the work output per cycle. To find the work output for the Carnot engine, you can use the formula for efficiency (η) of a Carnot engine, which is:
η = 1 - (Tc/Th)
where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir. Given that the Carnot engine operates between reservoirs at temperatures 704 K (Th) and 300 K (Tc), and it absorbs 100 J per cycle from the hot reservoir, we can substitute these values into the efficiency equation:
η = 1 - (300/704) = 1 - 0.4261 = 0.5739
The efficiency (η) tells us that 57.39% of the heat absorbed from the hot reservoir is converted into work. To find the actual work output per cycle, we multiply the efficiency by the heat absorbed:
Work output per cycle = η × Heat absorbed from the hot reservoir = 0.5739 × 100 J = 57.39 J
Therefore, the work output per cycle of the Carnot engine is 57.39 J.